Basic Math Examples

$\frac{x^{- \frac{1}{4}}}{x^{\frac{1}{3}} x^{\frac{1}{2}}}$

Step 1

Multiply $x^{\frac{1}{3}}$ by $x^{\frac{1}{2}}$ by adding the exponents.

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Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{- \frac{1}{4}}}{x^{\frac{1}{3} + \frac{1}{2}}}$

Step 1.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x^{- \frac{1}{4}}}{x^{\frac{1}{3} \cdot \frac{2}{2} + \frac{1}{2}}}$

Step 1.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x^{- \frac{1}{4}}}{x^{\frac{1}{3} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{3}{3}}}$

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{x^{- \frac{1}{4}}}{x^{\frac{2}{3 \cdot 2} + \frac{1}{2} \cdot \frac{3}{3}}}$

Step 1.4.2

Multiply $3$ by $2$ .

$\frac{x^{- \frac{1}{4}}}{x^{\frac{2}{6} + \frac{1}{2} \cdot \frac{3}{3}}}$

Step 1.4.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{x^{- \frac{1}{4}}}{x^{\frac{2}{6} + \frac{3}{2 \cdot 3}}}$

Step 1.4.4

Multiply $2$ by $3$ .

$\frac{x^{- \frac{1}{4}}}{x^{\frac{2}{6} + \frac{3}{6}}}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{x^{- \frac{1}{4}}}{x^{\frac{2 + 3}{6}}}$

Step 1.6

Add $2$ and $3$ .

$\frac{x^{- \frac{1}{4}}}{x^{\frac{5}{6}}}$

Step 2

Move $x^{- \frac{1}{4}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{\frac{5}{6}} x^{\frac{1}{4}}}$

Step 3

Multiply $x^{\frac{5}{6}}$ by $x^{\frac{1}{4}}$ by adding the exponents.

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Step 3.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{x^{\frac{5}{6} + \frac{1}{4}}}$

Step 3.2

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{x^{\frac{5}{6} \cdot \frac{2}{2} + \frac{1}{4}}}$

Step 3.3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{x^{\frac{5}{6} \cdot \frac{2}{2} + \frac{1}{4} \cdot \frac{3}{3}}}$

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{1}{x^{\frac{5 \cdot 2}{6 \cdot 2} + \frac{1}{4} \cdot \frac{3}{3}}}$

Step 3.4.2

Multiply $6$ by $2$ .

$\frac{1}{x^{\frac{5 \cdot 2}{12} + \frac{1}{4} \cdot \frac{3}{3}}}$

Step 3.4.3

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{1}{x^{\frac{5 \cdot 2}{12} + \frac{3}{4 \cdot 3}}}$

Step 3.4.4

Multiply $4$ by $3$ .

$\frac{1}{x^{\frac{5 \cdot 2}{12} + \frac{3}{12}}}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{1}{x^{\frac{5 \cdot 2 + 3}{12}}}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $5$ by $2$ .

$\frac{1}{x^{\frac{10 + 3}{12}}}$

Step 3.6.2

Add $10$ and $3$ .

$\frac{1}{x^{\frac{13}{12}}}$